Regularity problems for weak pushdown ω-automata and games

Abstract

We show that the regularity and equivalence problems are decidable for deterministic weak pushdown ω-automata, giving a partial answer to a question raised by Cohen and Gold in 1978. We prove the decidability by a reduction to the corresponding problems for deterministic pushdown automata on finite words. Furthermore, we consider the problem of deciding for pushdown games whether a winning strategy exists that can be implemented by a finite automaton. We show that this problem is already undecidable for games defined by one-counter automata or visibly pushdown automata with a safety condition. © 2012 Springer-Verlag.